%I #9 Feb 20 2022 01:26:41

%S 1,1,1,2,2,1,2,4,3,1,2,6,7,4,1,2,8,13,11,5,1,2,10,21,24,16,6,1,2,12,

%T 31,45,40,22,7,1,2,14,43,76,85,62,29,8,1,2,16,57,119,161,147,91,37,9,

%U 1,2,18,73,176,280,308,238,128,46,10,1,2,20,91,249,456

%N A129686 * A007318.

%C Row sums = A084215: (1, 2, 5, 10, 20, 40, 80, ...). A007318 * A129686 = A124725.

%C From _Philippe Deléham_, Feb 12 2014: (Start)

%C Riordan array ((1+x^2)/(1-x), x/(1-x)).

%C Diagonal sums are A000032(n) - 0^n (cf. A000204).

%C T(n,0) = A046698(n+1).

%C T(n+1,1) = A004277(n).

%C T(n+2,2) = A002061(n+1).

%C T(n+3,3) = A006527(n+1) = A167875(n).

%C T(n+4,4) = A006007(n+1).

%C T(n+5,5) = A081282(n+1). (End)

%F A129686 * A007318 (Pascal's Triangle), as infinite lower triangular matrices.

%F T(n,k) = T(n-1,k) + T(n-1,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = T(2,1) = 2, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Feb 12 2014

%e First few rows of the triangle:

%e 1;

%e 1, 1;

%e 2, 2, 1;

%e 2, 4, 3, 1;

%e 2, 6, 7, 4, 1;

%e 2, 8, 13, 11, 5, 1;

%e 2, 10, 21, 24, 16, 6, 1;

%e 2, 12, 31, 45, 40, 22, 7, 1;

%e 2, 14, 43, 76, 85, 62, 29, 8, 1;

%e 2, 16, 57, 119, 161, 147, 91, 37, 9, 1;

%e ...

%Y Cf. A129686, A007318, A124725.

%Y Cf. Columns: A046698, A004277, A002061, A006527, A006007, A081282

%K nonn,tabl

%O 0,4

%A _Gary W. Adamson_, Apr 28 2007

%E More terms from _Philippe Deléham_, Feb 12 2014